Question

If the degree of ionisation of a decimolar solution of a weak acid $HA$ is $0.01$ , then $p{K}_a$ of acid is:

• A. $2$
• B. $3$
• C. $5$
• D. $7$

Answer 1

The correct option is C $5$

The concentration $\left(C\right)$ of the solution is $=0.1\text{M}$
Degree of ionisation is $\alpha =0.01$
$\begin{array}{cccccc}& HA& \leftrightharpoons & H^{+}& +& A^{-}\\ t=0& C& & 0& & 0\\ t=t_{eq.}& C(1-\alpha )& & C\alpha & & C\alpha \end{array}$

$\therefore K_a=C{\alpha }^2=0.1\times (0.01{)}^2={10}^{-5}$
$\therefore p{K}_a=-\log K_a=-\log \left({10}^{-5}\right)=5$